An explicit harmonic code for black-hole evolution using excision

TL;DR

This paper introduces an explicit finite-difference code for simulating black hole evolution using excision, based on harmonic Einstein equations, validated through various tests including black hole mergers.

Contribution

The paper presents a new explicit, stable, and well-posed numerical code for black hole simulations using excision and harmonic formulation, with validation on complex scenarios.

Findings

Successful simulation of black hole evolution and mergers

Detection of apparent horizon touching and intersection during inspiral

Validation of code stability and accuracy across test cases

Abstract

We describe an explicit in time, finite-difference code designed to simulate black holes by using the excision method. The code is based upon the harmonic formulation of the Einstein equations and incorporates several features regarding the well-posedness and numerical stability of the initial-boundary problem for the quasilinear wave equation. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code. Such tests range from the evolution of isolated black holes to the head-on collision of two black holes and then to a binary black hole inspiral and merger. Besides assessing the accuracy of the code, the inspiral and merger test has revealed that individual apparent horizons can touch and even intersect. This novel feature in the dynamics of the marginally trapped surfaces is unexpected but consistent with theorems on the properties of apparent horizons.